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5th Grade Math Element Cards

September 2014Revised December 2016

Element Card

FLS: MAFS.5.OA.1.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

MAFS.5.OA.1.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Access Point NarrativeMAFS.5.OA.1.AP.1a Evaluate a simple expression involving one set of

parentheses.MAFS.5.OA.1.AP.2a Write a simple expression for a calculation.

Essential Understandings:Access Point Concrete Understandings Representation

MAFS.5.OA.1.AP.1a Identify the operation to be completed first as shown by parenthesis placement.

Use manipulatives and a frame, jig, or template to model the steps of an expression.to find the value.

Understand the concepts and vocabulary for parentheses ( ), equations, =, +, -, ÷, x.

Use visual representation to model expressions.

MAFS.5.OA.1.AP.2a Use manipulatives and a frame, jig, or template to express the calculation. (i.e. “add 8 and 7”).

Understand the concepts and vocabulary for parentheses ( ), equations, =, +, -, ÷, x.

Use visual representation to model an expression.

Suggested Instructional Strategies: Explicit instruction on order of operations when a two-step expression has

one set of parentheses. At this grade level, focus only on the fact that the operation in parentheses must be performed first, and then the second operation in the expression may be performed, regardless of their order in the expression.

Task Analysis of evaluating a simple expression involving one set of parentheses:

o Provide the student with a simple numerical expression involving one set of parentheses (e.g., (3+5) x 7 or 9 ÷ (4-1)).

o The student will say/select/indicate the operation that is to be performed first (the one in the parentheses) and point/gaze at the operational sign that indicates that operation.

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Element Cardo The student will use manipulatives to perform that operation (this part

of the expression can now be highlighted/crossed out to show that the operation has already been performed.)

o The student will say/select/indicate the operation that is to be performed next (the one outside of the parentheses) and point/gaze at the operational sign that indicates that operation.

o The student will use manipulatives to perform that operation to the results of the first calculation (e.g., for the expression (3+5) x 7, if (3+5) was done in the first step to get the sum of 8, 8 x 7 should be done in the second step.)

*Do not use an equal sign to indicate the value of the expression. Only equations have equal signs.

Task Analysis for writing a simple expression:o Give the student a description of a simple calculation in words (e.g.,

add three and two, divide nine by three, four multiplied by eight, etc.)o The student will say/select/indicate the numbers involved in the

calculation (e.g., 3 and 2, 9 and 3, 4 and 8). The student will place (with support, as needed) digit cards in a graphic organizer for creating a simple expression (e.g., three boxes, three blanks, three columns, etc. one for each number and one for the operational sign in the middle)

o The student will say/select/indicate the operation (e.g., addition, division, multiplication, etc.) The student will place (with support, as needed) a card labeled with the correct operational sign between the numbers in the graphic organizer for creating a simple expression.

o The numerical expression should be related back to the verbal description of the calculation to check for accuracy.

*Important note: these calculations DO NOT have to actually be made. Expressions do not have equal signs.

Supports and Scaffolds: Brainpop.com video on order of operations and exponents Manipulatives as needed Calculator Graphic organizer for creating simple expressions Assistive technology iPad applications Interactive Whiteboard Digit cards/cards with operational symbols

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FLS: MAFS.5.OA.2.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Access Point NarrativeMAFS.5.OA.2.AP.3a Given two pattern descriptions involving the same context (e.g.,

collecting marbles), determine the first five terms and compare the values.

Essential Understandings:Concrete Understandings Representation

Use manipulatives to complete a pattern in a table.

Identify a numeric pattern given a data set in a table.

Suggested Instructional Strategies: Provide the students with a rule (e.g., add 2 for Joe and add four for Kim.)

Relate the rule to a context and help the student visualize the context. Use manipulatives to show the student how the rule is progressing based on

the terms that are already included on the chart. After observation, the student will extend each pattern 5 terms using

manipulatives and direct modeling (e.g., Joe had 10 marbles, so count out ten counters, then the rule is add two, so count out two more counters, and then count the total number of counters to find the next term in the pattern: 12.)

Encourage the student to look for relationships between the two patterns (multiplying Joe’s number of marbles by 2 to get Kim’s number of marbles.)

Supports and Scaffolds: Counters iPad application Assistive technology Interactive Whiteboard

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FLS: MAFS.5.OA.2.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.MAFS.5.G.1.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

MAFS.5.G.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Access Point NarrativeMAFS.5.G.1.AP.1a Locate the x- and y-axis on a coordinate plane.MAFS.5.G.1.AP.1b Locate points on a coordinate plane.MAFS.5.G.1.AP.1c Graph ordered pairs (coordinates).MAFS.5.G.1.AP.2a Find a location on a map using given coordinates.MAFS.5.OA.2.AP.3b Graph ordered pairs on a coordinate plane when given a

table that follows pattern rules.


MAFS.5.G.1.AP.1a Identify the x- and y-axes on a tactile (i.e., raised gridlines) graph.

Identify the origin (i.e., point of intersection of the x- and y-axes) on a tactile graph.

Understand the following concepts and vocabulary: x-axis, y-axis, graph, origin, point of intersection, horizontal, and vertical.

Identify the x- and y-axes on a graph.

MAFS.5.G.1.AP.1b Identify the x- and y-axes. Identify the origin (i.e., point

of intersection of perpendicular lines).

Locate a given point on a coordinate plane (e.g., show me point A).

Use tools (e.g., use craft sticks to extend the point to the axis) to identify an ordered pair as an x-coordinate followed by a y-

Understand the following concepts and vocabulary: origin, axis, grid, point, x-axis, y-axis, point of intersection.

Identify an ordered pair as an x-coordinate followed by a y-coordinate.

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Element CardAccess Point Concrete Understandings Representation

coordinate.MAFS.5.G.1.AP.1c Identify the x- and y-axes.

Identify the origin (i.e., point of intersection of perpendicular lines).

Identify that an ordered pair:o The first coordinate is the

location on the x-axis.o The second coordinate is

the location on the y-axis.o The coordinates are

written in parentheses and separated by a comma (3,2).

Complete concrete graphing of ordered pairs (e.g., use a manipulative to move 3 spaces across the x-axis, then 2 spaces up the grid; mark the point).

Understand the following concepts and vocabulary: coordinates, ordered pair, origin, axis, grid, point, parentheses, and comma.

Graph ordered pairs on a coordinate plane.

MAFS.5.G.1.AP.2a Identify the x- and y-axes on a map.

Identify the origin (i.e., point of intersection of perpendicular lines) on a map.

Locate a given point on a map (e.g., show me point A on the map).

Use tools (e.g., use craft sticks to extend the point to the axis) to identify an ordered pair as an x-coordinate followed by a y-coordinate.

Understand the following concepts and vocabulary: coordinates, ordered pair, origin, axis, grid, point, up, down, over

Given a visual diagram, locate the coordinate values of an item.

Use a map to find a given location.

MAFS.5.OA.2.AP.3b Continue a pattern on a graph when the first two sets of ordered pairs are graphed.

Demonstrate an understanding of the concepts, symbols and vocabulary of graph, +, -.

Write the ordered pairs from information provided in the table.

Graph ordered pairs from a provided table.

Suggested Instructional Strategies: Teach explicitly through a hands-on graphing activity as provided by CPALMS

Click here for link Teach explicitly the components, vocabulary associated with, and how to

label a coordinate plane including:

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Element Cardo Coordinates – a group of numbers used to indicate the position of a

point, line, or plane.o Ordered pair – a pair of numbers where order is important – (4, 6) ≠ (6,

4) and are used to indicate a point on a graph or map.o Origin – the point where the x- and y-axis intersect on a coordinate

plane.o Axis – a fixed reference line for the measurement of coordinates.o Grid – an object (paper, geoboard) marked with regular lines

(horizontal and vertical) used for graphing.

o Create a giant coordinate grid on the floor in your classroom (his works very well if you have a tile floor.)

o Mark the grid with painter’s tape and use index cards to number the x-axis and y-axis.

o Place dots with student names on the giant coordinate grid.o Call the students by name to prevent a mad rush. Tell them that when

you call their name they are to walk over and stand on their dot.o Ask one student to raise their hand and teacher walks to the big “0,0”

for the origin and ask, “What do I need to do to reach Chelsea?” Give students a few minutes to process, then explain “To reach Chelsea, I have to walk 5 units along the x-axis (think of the x as across because the lines cross), and now 3 units up. If you look at the y-axis you should be in line with the 3 on the y-axis, (tell them to think y to the sky!”)

o As they are taking their turns keep asking, “Which way do you move first? Which way do you move second? When you move along what axis are you on? When you move up what axis are you in line with?”

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Use a child friendly map to instruct children on finding coordinates on a map (e.g., (F,7) is the pig.)

Link to image

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Element Card Given a table of ordered pairs, students will be able to translate data into

coordinate points. (e.g., so coordinate points would be (0,3) (1,4) (2,5) (3,6) (4,7))

x y0 31 42 53 64 7

Supports and Scaffolds: Assistive technology Interactive Whiteboard Painters tape Child friendly map Geoboard Locating points on a coordinate plane: Click here Locate the “aliens” on a coordinate plane: Click here Graph points on a coordinate plane: Click here You Sank my Battleship! Online tutorial for understanding coordinates: Click

here

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FLS: MAFS.5.NBT.1.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Access Point NarrativeMAFS.5.NBT.1.AP.1a Compare the value of a number when it is represented in different

place values of two three-digit numbers.


Given two models of base ten blocks on a place value chart, compare the value of the same digit used in different place value positions (e.g., 123 where 2 represents 2 tens and 142 where 2 represents 2 ones).

Recognize the value of a digit based on its place in a three-digit number (e.g., the 2 in 125 represents 2 tens or 20).

Compare the value of the same digit used in different place value positions (e.g., 123 where 2 represents 2 tens and 142 where 2 represents 2 ones).

Suggested Instructional Strategies: Use a base ten block to model two different numbers on a place value chart

with one-digit that is in common, but in different place values (e.g., 231 and 425 both have a 2, but it is in different place values) and then compare the blocks that represent the same digit to see which is greater and which is lesser (e.g., 2 hundred flats is 10 times greater than 2 ten rods.)

Use a visual representation, such as a straw activity. Use a pocket chart with hundreds, tens, and ones pockets. Put a specified number of straws in the ones pocket (e.g., 23). Have students count out 10 straws and then bundle with a rubber band and place in the tens. For 23, students should bundle two sets of 10 and place in tens pocket and have three straws left in the ones pocket. Do the same in another pocket chart with a different number that has one digit in common with the first, but in a different place value pocket (e.g., 23 and 42). Then, remove the items from the pockets that share the same digit and compare them to see which is greater and which is lesser (e.g., two bundles of 10 straws is ten times greater than two single straws).

Teach using a place value chart with the hundreds, tens, and ones of each number labeled within the chart. Have the student identify the digit that the numbers have in common and compare those digits based on their place value (e.g., the higher the place value, the greater the value of the digit).

Teach in the context of money using a place value chart (e.g., using one hundred dollar bills, ten-dollar bills, and one-dollar bills). Compare a common digit of two monetary values that is in different denominations (e.g., 5 hundreds compared to 5 tens) to determine which is greater and which is lesser (e.g., 5 hundreds is ten times greater than 5 tens.)

Supports and Scaffolds: Place value chart Items that can be bundled

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Element Card Play money Interactive Whiteboard or other technology to manipulate representations

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FLS: MAFS.5.NBT.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.MAFS.6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents.

Access Point NarrativeMAFS.5.NBT.1.AP.2a Identify what an exponent represents (e.g., 10³ = 10 × 10 × 10).MAFS.6.EE.1.AP.1b Identify what an exponent represents (e.g., 8³ = 8 x 8 x 8).


MAFS.5.NBT.1.AP.2a Locate the exponent on a given number.

Use manipulatives or objects to demonstrate exponents.

Use repeated addition or multiplication to solve for the total value of a number with an exponent.

Understand the following concepts, symbols, and vocabulary for exponents: ×, exponent.

MAFS.6.EE.1.AP.1b Produce the correct amount of base numbers to be multiplied given a graphic organizer or template.

Select the correct expanded form of what an exponent represents (e.g., 8³ = 8 × 8 × 8).

Identify the number of times the base number will be multiplied based on the exponent.

Understand the following concepts, symbols, and vocabulary: base number, exponent.

Suggested Instructional Strategies: Create diagram or number tree Task Analysis

o Identify the exponent of a numbero Identify the number o Write the number, the number of times indicated by the exponent

Supports and Scaffolds: Circle or highlight the raised number (exponent) Graphic organizer

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FLS: MAFS.5.NBT.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Access Point NarrativeMAFS.5.NBT.1.AP.2b Identify the direction the decimal point will move when

multiplying or dividing by a power of 10.

Essential Understandings:Concrete Understandings Representation Understand left and right. Understand the structure

of a decimal, including the place value patterns.

Count to 100.

Understand the concepts, symbols, and vocabulary for exponents: x, exponent.

Understand place value to the hundreds and hundredths.

Understand where to write a decimal point. Understand the following concepts, symbols,

and vocabulary: decimal, decimal point, tens place, hundreds place, tenths place, hundredths place.

Suggested Instructional Strategies: Task Analysis for multiplying by ten:

o Use individual digit cards and a counter to represent a single digit number as a decimal number (e.g., 3 would be 3.0).

o Show the student a multiplication equation that shows the current number being multiplied by 10 (e.g., 3.0 x 10= 30.0).

o Have the student move the decimal point to turn the current number into the number it would be if it were multiplied by 10 (e.g., 3.0 would become 30.0 by moving the decimal point one place to the right.)

o Show the student a multiplication equation that shows the new number being multiplied by 10 (e.g., 30.0 x 10=300.0).

o Have the student move the decimal point to turn the new number into the number it would be if it were multiplied by 10 (e.g., 30.0 would become 300.0 by moving the decimal point another place to the right.)

o Repeat steps until the pattern, that every time the number is multiplied by 10 the decimal point moves one place to the right, is evident. Help the student recognize this pattern and when prompted, indicate which direction the decimal point moves when multiplying by 10.

Task Analysis for dividing by ten:o Use individual digit cards and a counter to represent a multi-digit

number as a decimal number (e.g., 3,000 would be 3,000.0).o Show the student a multiplication equation that shows the current

number being divided by 10 (e.g., 3,000.0 ÷ 10= 300.0).

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Element Cardo Have the student move the decimal point to turn the current number

into the number it would be if it were multiplied by 10 (e.g., 3,000.0 would become 300.0 by moving the decimal point one place to the left.)

o Show the student a multiplication equation that shows the new number being divided by 10 (e.g., 300.0 ÷10= 30.0).

o Have the student move the decimal point to turn the new number into the number it would be if it were divided by 10 (e.g., 300.0 would become 30.0 by moving the decimal point another place to the left.)

o Repeat steps until the pattern, that every time the number is divided by 10 the decimal point moves one place to the left, is evident. Help the student recognize this pattern and when prompted, indicate which direction the decimal point moves when dividing by 10.

Supports and Scaffolds: Digit cards Counter Equation cards Calculator Assistive technology iPad applications Interactive Whiteboard

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FLS: MAFS.5.NBT.1.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number

names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Access Point NarrativeMAFS.5.NBT.1.AP.3a Read, write, or select a decimal to the hundredths place.MAFS.5.NBT.1.AP.3b Compare two decimals to the hundredths place, whose

values are less than one.


MAFS.5.NBT.1.AP.3a Recognize part/whole when materials are divided into tenths.

Count tenths to determine how many (e.g., four tenths; 0.4 have the decimal present but student is not required to read).

Count to 100. Understand place value to

the hundredths. Understand where to write a

decimal point. Understand concepts,

symbols and vocabulary: decimal, decimal point, tenths place, hundredths place.

MAFS.5.NBT.1.AP.3b Recognize parts of a whole using materials divided into hundredths.

Understand the structure of a decimal, including the place value patterns.

Understand that numbers to the right of the decimal represent a value less than one.

Compare various amounts of change when making purchases, and determine which amount is larger.

Know value of places to the thousandths.

Understand where to write a decimal point (e.g., to the right of the units).

Understand the following concepts, symbols, and vocabulary: decimal, decimal point, hundredths, hundredths place, thousandths, thousandths place.

Suggested Instructional Strategies: Teach explicitly how the position of a digit after the decimal point relates to

its value. (e.g., a digit one place to the right of the decimal point represents 1/10, so whatever digit is in that place value position is worth that number of tenths: a 3 in the tenths place has a value of 3 tenths.)

Teach explicitly how to read decimals to the tenths (0.1) and hundredths (0.01) by using a place value chart (e.g., when digit cards are used to build a decimal number on a place value chart, if there is only a 4 in the tenths column, then the number is 4 tenths or 0.4, and if there is a 2 in the tenths column and a 6 in the hundredths column, then altogether there are 26 hundredths or 0.26.)

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Element Card Teach explicitly how to write/show decimals to the tenths (0.1) and

hundredths (0.01) by using a place value chart (e.g., when the decimal number is read aloud, digit cards are used to represent the number in order to show the appropriate amount in each place value: Four-tenths should be represented by a 4 in the tenths place, which is 0.4, and nineteen-hundredths should be represented by a one in the tenths place and a nine in the hundredths place so that the number nineteen extends into the hundredths place, which is 0.19.)

Task Analysis for decimals (tenths)o Present a 1 x 10 grid and ask the student how many boxes make up

the grid.o Shade a tenth and ask how many boxes are shaded (i.e., 1 out of 10).o Ask the student to write or select a written form for the decimal that

represents 1/10.o Ask the student to read or select a recording of the decimal that

represents 1/10.o Complete for multiple decimals (0.1 - 0.9).

Task Analysis for decimals (hundredths)o Present a 10 x 10 grid and ask the student how many boxes make up

the grid.o Shade ten hundredths and ask how many boxes are shaded (i.e., 10

out of 100).o Ask the student to write or select a written form for the decimal that

represents 10/100.o Ask the student read or select a recording of the decimal that

represents 10/100.o Complete for multiple decimals (0.10-0.99 and then 0.01-0.09)

Using a place value chart, relate decimals to money amounts that are written as decimals of a dollar (e.g., the ones place represents the number of one dollar bills, the tenths place represents the number of dimes because they are 1/10 of a dollar, and the hundredths place represents the number of pennies because they are 1/100 of a dollar.)

Click for image link

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http://www.free-math-handwriting-and-reading-worksheets.com/

Element Card *Non-Example: show a labeled model of a decimal that extends to the

hundredths place but does not have a digit in the tenths place, such as 1/100 or 0.01, and a labeled model of a commonly confused representation of that number, such as 0.1 or 1/10, to show that they are different. This can also be done with base ten blocks.

Task Analysis for comparing decimals to tenths with visual models:o Provide two 1 x 10 grids.o On the first grid, shade a tenth and ask how many boxes are shaded

(i.e., 1 out of 10).o Ask the student to write or select a written form for the decimal that

represents 1/10.o On the second grid, shade two tenths and ask how many boxes are

shaded (i.e., 2 out of 10).o Ask the student to write or select a written form for the decimal that

represents 2/10.o Ask the student to say or select the decimal that is greater and the

decimal that is lesser.o Complete for multiple decimals (0.1 - 0.9).

Task Analysis for comparing decimals to hundredths with visual models:o Provide two 10 x 10 grids.o On the first grid, shade nineteen hundredths and ask how many boxes

are shaded (i.e., 19 out of 100).o Ask the student to write or select a written form for the decimal that

represents 19/100.o On the second grid, shade twenty-one hundredths and ask how many

boxes are shaded (i.e., 21 out of 100).o Ask the student to write or select a written form for the decimal that

represents 21/100.o Ask the student to say or select the decimal that is greater and the

decimal that is lesser.o Complete for multiple decimals (0.1 - 0.9).

Use two place value charts (lined up directly above and below each other) to model decimal numbers to tenths or hundredths with digit cards or base ten blocks. Have the student compare the values of the digits starting with the greatest place value position in order to identify which decimal is greater and which is lesser.

Relate decimals to money amounts that are written as decimals of a dollar and have students determine which money amount is greater and which is lesser. Model with play money (dimes and pennies), if necessary.

Help students locate both decimal numbers to tenths on the same number line and use their location on the number line to help determine which number is greater and which is lesser.

Suggested Supports and Scaffolds: Place Value Mat

o Click here to visit site for an example

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Element Card Word cards, number cards, and grid cards for the same decimals

(e.g., one tenth, 0.1, and a model) 1 x 10 and 10 x 10 grid paper Assistive technology Number Line Base Ten blocks Play money (dimes and pennies)

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FLS: MAFS.5.NBT.1.4 Use place value understanding to round decimals to any place.

Access Point NarrativeMAFS.5.NBT.1.AP.4a Round decimals to the nearest whole number.MAFS.5.NBT.1.AP.4b Round decimals to the tenths place.MAFS.5.NBT.1.AP.4c Round decimals to the hundredths place.


MAFS.5.NBT.1.AP.4a Understand that numbers to the right of the decimal represent a value less than one.

Use rules for rounding with whole numbers.o If last number is five or more,

round to the next highest whole number.

o If the last number is four or less, round to the next lowest whole number.

Use change to represent less than one with one being a dollar.

Make comparisons between similar/different with concrete representations (i.e., is this set of manipulatives [8 ones] closer to this set [a 10] or this set [a one]?

Understand the following vocabulary:o Fraction (a/b) o Decimal (.a)o Tenths place (.a)o Hundredths place (.aa)

MAFS.5.NBT.1.AP.4b Use rules for rounding.o If last number is five or more,

round to the next highest tenth.

o If the last number is four or less, round to the next lowest tenth.

Identify “tenths” on a number line between 0 and 1.

Make comparisons between similar/different with concrete representations (i.e., is this set of manipulatives [8 ones] closer to this set [a 10] or this set [a one]?

Understand the following vocabulary:o Fraction (a/b) o Decimal (.a)o Tenths (.1)o Hundredths (.10)

MAFS.5.NBT.1.AP.4c Estimate with decimals. Demonstrate understanding that

we are estimating whether the number is closest to the next lowest or next highest specified place (e.g., 0.45 to the nearest tenth).

Understand the following concepts, symbols, and vocabulary: decimal, decimal point, round, hundredths, hundreds place, thousandths, thousandths place.

Suggested Instructional Strategies: Task Analysis for rounding to the nearest whole number (the number to be

rounded should extend to the tenths place):

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Element Cardo Provide the student with a number line labeled with the two whole

numbers that the number to be rounded is between (e.g., if the number is 8.7, the number line should be between 8 and 9) that has been divided into tenths with each tenth labeled. The student will identify the whole numbers: 8 and 9. (Use *Constant Time Delay (CTD) Prompts, if necessary.)

o The halfway point (e.g., for 8 and 9, 0.85) should be marked in a distinct way (possibly in a different color). The student will identify the halfway point (this will be used as a benchmark to help the student round.)

o The student will use a counter, sticker, stamp, etc. to visibly place the number to be rounded on the number line.

o The student will say/select the whole number that the number to be rounded is closest to on the number line. Counting tick marks from the lesser whole number to the number and from the number to greater whole number (to see which is a lesser number of tenths away) may be done if the student is struggling to use the halfway point to determine which whole number the number is closer to on the number line.

Task Analysis for rounding to the nearest tenth (the number to be rounded should extend to the hundredths place):

o Provide the student with a number line labeled with the two tenths that the number to be rounded is between (e.g., if the number is 0.29, the number line should be between 0.2 and 0.3 that has been divided into hundredths with each hundredth labeled. The student will identify the tenths: 0.2 and 0.3. (Use *Constant Time Delay (CTD) Prompts, if necessary).

o The halfway point (e.g., 0.25 for 0.2 and 0.3) should be marked in a distinct way (possibly in a different color). The student will identify the halfway point (this will be used as a benchmark to help the student round.)


o The student will say/select the tenth that the number to be rounded is closest to on the number line. Counting tick marks from the lesser tenth to the number and from the number to the greater tenth (to see which is a lesser number of hundredths away) may be done if the student is struggling to use the halfway point to determine which tenth the number is closer to on the number line.

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Element Card Task Analysis for rounding to the nearest hundredth (the number to be

rounded should extend to the thousandths place):o Provide the student with a number line labeled with the two

hundredths that the number to be rounded is between (e.g., if the number is 0.456, the number line should be between 0.40 and 0.50 that has been divided into thousandths with each thousandth labeled. The student will identify the hundredths: 0.40 and 0.50.) (Use *Constant Time Delay (CTD) Prompts, if necessary.)

o The halfway point (e.g., 0.450 for 0.40 and 0.50) should be marked in a distinct way (possibly in a different color). The student will identify the halfway point (this will be used as a benchmark to help the student round.) (Use *Constant Time Delay (CTD) Prompts, if necessary).


o The student will say/select the hundredth that the number to be rounded is closest to on the number line. Counting tick marks from the lesser hundredth to the number and from the number to the greater hundredth (to see which is a lesser number of hundredths away) may be done if the student is struggling to use the halfway point to determine which tenth the number is closer to on the number line.

Supports and Scaffolds: Number Line Interactive Whiteboards or other technology to manipulate representations Graphic organizer or place value template Apply quantities to coin values for a real world application (e.g., 28₵ rounds

up to 30₵.)

3

Element Card

FLS: MAFS.5.NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Access Point NarrativeMAFS.5.NBT.2.AP.5a Fluently multiply two-digit numbers.


Use base ten blocks to perform repeated addition

Use objects or manipulatives to create arrays

Use visual representations to solve problems. Understand the process of carrying and borrowing

when adding and subtracting. Understand the concepts, symbols, and vocabulary for

+, - , =.Suggested Instructional Strategies:

Task Analysis for multiplying with two-digit numbers:o Student uses base ten blocks to cover a premade visual of an array for

two-digit-by-two-digit multiplication on a template. (See visual below.) o As each base ten block manipulative is place on visual, use prompting

to help the student identify the multiplication expression shown by each array.

o Student uses a multiplication table to find the product of each array. o Student selects the card labeled with each product and labels each

array with the product of that array.o The student adds the product of each array to find the product of the

total array (a calculator may be used, if necessary)o Student relates the concrete model to a written method called partial

products (the cards labeled with the products used for the multiplication array can be used to show each step.)

Supports and Scaffolds: Base Ten Rods Templates Labeled product cards Multiplication table Assistive technology iPad applications Interactive Whiteboard Calculator

1

Element Card

FLS: MAFS.5.NBT.2.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Access Point NarrativeMAFS.5.NBT.2.AP.6a Find whole number quotients up to two dividends and two

divisors.MAFS.5.NBT.2.AP.6b Find whole number quotients of whole numbers with up to

two-digit dividends and two-digit divisors.


MAFS.5.NBT.2.AP.6a Decompose (÷) with concrete objects; use counting to get the answers.

Match the action of decomposing with vocabulary (i.e., divide or separate into groups).

Understand concept of division: sharing or grouping numbers into parts.

Understand the concepts symbols and vocabulary of division, part, whole, divisor, quotient, ÷, =, —).

Use a visual representation of dividends and divisors.

MAFS.5.NBT.2.AP.6b Decompose (÷) with concrete objects; use counting to get the answers.

Match the action of decomposing with vocabulary (i.e., divide or separate into groups).

Understand concept of division: Sharing or grouping numbers into parts.

Understand the concepts, symbols, and vocabulary of division, part, whole, divisor, quotient, ÷, =, —).

Suggested Instructional Strategies: Task Analysis for division that does not require regrouping of tens:

o Student uses base ten manipulatives to model the dividend of division expressions that do not require regrouping of tens (e.g., 63 divided by 3 does not involve regrouping because you can put 2 ten rods in each of 3 groups and then you can put 3 one cubes in each of the 3 groups because the value of each place is divisible by the divisor). Division expressions should not results in quotients with remainders.

1

Element Cardo Student solves problem as partitive division (division problems where

the divisor indicates the number of groups the dividend is to be divided into) by dividing the dividend into the number of equal groups indicated by the divisor (e.g., 84 divided by 4 would involve dividing the base ten blocks representing 84 into 4 equal groups). Relate partitive division to fair sharing. Ten can be shared and then ones can be shared, or vice versa. Use a template to show where each group is located.

o Student counts/calculates the number in one group, and this number is the quotient.

Task Analysis for division that requires regrouping of tens:o Student uses individual counters to model the dividend of division

expressions that require regrouping (e.g., 24 divided by 12 involves regrouping because there are not enough tens to put equally into 12 groups, so you have to regroup the tens into ones). Division expressions should not result in quotients with remainders.

o Student solves problem as partitive division (division problems where the divisor indicates the number of groups the dividend is to be divided into) by dividing the dividend into the number of equal groups indicated by the divisor (e.g., 56 divided by 14 would involve dividing the base ten blocks representing 56 into 14 equal groups). Relate partitive division to fair sharing and divvy the counters out one at a time. Use a template to show where each group is located.

o Student counts the number in one group, and this number is the quotient.

*Real world items such as candy, cookies, snacks, etc. can be used to illustrate partitive division as fair sharing.

Supports and Scaffolds: Use a calculator Interactive Whiteboards or other technology to manipulate representations Provide meaningful manipulatives or picture representations with symbols

included Multiplication and division tables Base Ten Blocks Templates Items that can be shared in fair shares such as candy, cookies, snacks, etc.

2

Element Card

FLS: MAFS.5.NBT.2.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Access Point NarrativeMAFS.5.NBT.2.AP.7a Solve one-step problems using decimals.


Given a real-world context, determine when to add, subtract, multiply, and divide.

Understand that numbers to the right of the decimal represent a value less than one.

Follow rules for decimal point placement when adding, subtracting, multiplying, or dividing.

Understand symbols for +, -, ×, ÷.

Know the following vocabulary: decimal point, decimal.

Suggested Instructional Strategies: Teach problem-solving strategies to determine operations. Use task analytic instruction to teach steps to solve word problems. Teach using *Least-to-Most Prompts Use *Model/Lead/Test Have students self-check their answers. Start by modeling this process. To demonstrate addition, gather several representations labeled with the

decimal (circles, squares, pattern blocks, Cuisenaire rods) and identify how many of the pieces make one whole (e.g., 0.5 + 0.5).

Supports and Scaffolds: 10 x 10 hundreds grids Place value chart Calculator Assistive technology Interactive Whiteboard Computer software

1

Element Card

FLS: MAFS.5.NF.1.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Access Point NarrativeMAFS.5.NF.1.AP.1a Add and subtract fractions with like denominators with

sums greater than one represented by mixed numbers using visual fraction models.


To add, use fraction manipulatives (each piece may be labeled with the corresponding unit fraction) to model each fraction and join them to find the sum (e.g., 3/4 + 2/4 = 5/4).

To subtract, use fraction manipulatives (each piece may be labeled with the corresponding unit fraction) to model the first number in the expression and remove manipulatives that represent the fraction being subtracted(e.g. 5/4 - 2/4 = 3/4)

To add, use a visual representation of a whole divided into equal pieces (each piece may be labeled with the corresponding unit fraction). Shade each unit to represent the fractions in the expression and count the shaded units to find the sum.

To subtract, use a visual representation of the first fraction in the expression. Cross out the piece(s) that represent the fraction being subtracted. Count the remaining piece(s) to find the remainder.

Understand the following vocabulary: fraction, numerator, denominator, fraction greater than one, mixed number.

Suggested Instructional Strategies: *Model/Lead/Test

1

Element Card

ModelSteps/Materials Teacher Says/Does Student

ResponseTeacher Feedback

Teacher:Fraction Bars

“I can use fraction bars to add fractions.”Lay down fraction bars. Point to, count, and name each fraction separately. (e.g. For the addition expression 3/4 + 2/4, lay down three ¼ pieces and then two ¼ pieces separately then point and count ¼, 2/4, 3/4 for the first fraction and ¼, 2/4 for the second fraction).

Student watches.

“Good watching me.”

Demonstrate joining the two separate fractions. Point and count each unit fraction (e.g. ¼, 2/4, ¾, 4/4, 5/4) and then say the addition equation (e.g. ¾ plus 2/4 equals 5/4).

Student watches.


Place a fraction bar that represents one whole directly above the fraction bars representing the sum. Say, “These pieces equal to one whole and there are also some pieces left over.” Rename the fraction greater than one as a mixed number. (e.g., 4/4 is the same length as one whole and there is one ¼ left over, so the mixed number is 1 ¼).

Student watches.


2

Element CardSteps/Materials Teacher Says/Does Student Response Teacher

FeedbackTeacher and Student: Fraction Bars

“We can use fraction bars to add fractions.”Lay down fraction bars. Point to, count, and name each fraction separately. (e.g. For the addition expression 3/4 + 2/4, lay down three ¼ pieces and then two ¼ pieces separately then point and count ¼, 2/4, 3/4 for the first fraction and ¼, 2/4 for the second fraction).

Student lays down fraction bars to show the same fractions modeled by teacher. Student points to/says each separate fraction.

“Good job.”

Demonstrate joining the two separate fractions. Point and count each unit fraction (e.g. ¼, 2/4, ¾, 4/4, 5/4) and then say the addition equation (e.g. ¾ plus 2/4 equals 5/4).Say, “Now, you join the fractions to find the sum”.

Student joins two separate fractions to show the addition equation. Say/select the correct sum (e.g. 2/4).

“Good job joining the fractions to find the sum.”

Place a fraction bar that represents one whole directly above the fraction bars representing the sum. Say, “These pieces equal to one whole and there are also some pieces left over.” Rename the fraction greater than one as a mixed number. (e.g., 4/4 is the same length as one whole and there is one ¼ left over, so the mixed number is 1 ¼).Say, “Now, you rename the fraction greater than one as a mixed number.”

Student places a fraction bar that represents one whole directly above the fraction bars representing the sum. Renames/selects the fraction greater than one as a mixed number.

“Good job renaming the fraction greater than one as a mixed number.”

Lead

3

Element CardSteps/Materials Teacher Says/Does Student Response Teacher

FeedbackStudent: Fraction Bars

“You can use fraction bars to add fractions.”Say, “Now, you show the fractions in the addition expression.”

Student lays down fraction bars to show the fractions requested by teacher. Student points to/says each separate fraction.

“Good job.”

Student makes an incorrect response or no response.

“Watch me” and model the correct response, then have the student complete it correctly.

Say, “Add your fractions. Student joins two separate fractions to show the addition expression. Say/select the correct sum (e.g. 5/4).

“Good job joining the fractions to find the sum.”



Say, “Now, you rename the fraction greater than one as a mixed number.”

Student places a fraction bar that represents one whole directly above the fraction bars representing the sum. Renames/selects the fraction greater than one as a mixed number.

“Good job renaming the fraction greater than one as a mixed number.”



Test

4

Element CardRepeat the *Model/Lead/Test to subtract fractions with like denominators where the fraction being subtracted from is represented by a mixed number. Remove fraction bars instead of joining fraction bars.

Pizza Fractions: Cut pizza circles the same size then cut them and label them with a variety of unit fractions. Use them to add fractions with like denominators that result in sums greater than one (represented as mixed numbers) and to subtract fractions with like denominators where the fraction being subtracted from is represented by a mixed number (e.g., join one 1/2 pizza to three 1/2 pieces to make 2 wholes or remove one 1/3 pizza from four 1/3 pieces, put together to show 1-1/3, to leave 1 whole pizza.)

Supports and Scaffolds: Fraction bars Number Lines representing 0-2 with each whole divided into the same

number of pieces as the denominator of the fractions being added or subtracted

Pictorial representations where the wholes are the same size Assistive technology Interactive Whiteboard Computer software Pattern blocks or sets of objects Representations of fractions with raised sections

5

Element Card

FLS: MAFS.5.NF.1.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Access Point NarrativeMAFS.5.NF.1.AP.1b Add or subtract fractions with unlike denominators within one whole unit

on a number line.Essential Understandings:

Concrete Understandings Representation Use manipulatives to represent fractions. Use manipulatives to combine fractions within 1. Click here Use manipulatives to separate fractions within 1. Click here Use a number line to represent fractions.

Use a number line to combine fractions within 1.

Use a number line to separate fractions within 1.

Suggested Instructional Strategies: Task Analysis:

o Provide the student with a number line that represents 0-1 and is pre-divided into the same number of equal parts (the parts should be the same length as the fraction bar that represents that sized part) as the least common denominator of the fractions being added (e.g., for the addition expression 1/2 + 1/4, give the student a number line that is divided into parts that are the same size as the 1/4 fraction bar piece.)

o Starting at 0, place fraction bars that represent the first fraction above the number line and point out that the fraction bar(s) ends in the same place as the fraction labeled on the number line, so those two fractions are equal (e.g., the 1/2 fraction bar is the same length as 2/4 on the number line, so they are equivalent fractions.)

o Starting at the end of the first fraction, place fraction bars that represent the second fraction above the number line. Show the student that the length of the two fractions added together is from 0 to where the joined fractions end and that the label for this point on the number line is the sum of the two fractions.

*Repeat the task analysis for subtraction of fractions with unlike denominators within one unit.

Suggested Supports and Scaffolds: Number Lines Fraction bars Assistive technology Interactive Whiteboard Computer software

1

https://learnzillion.com/lessons/974-subtract-fractions-with-different-denominators-using-fraction-bars

https://learnzillion.com/lessons/973-add-fractions-with-different-denominators-using-fraction-bars

Element Card

FLS: MAFS.5.NF.1.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Access Point NarrativeMAFS.5.NF.1.AP.2a Solve word problems involving the addition and subtraction

of fractions using visual fraction models.


Match the vocabulary in a word problem to an action.

Use manipulatives to model the context of the word problem.

Count to find the answer. To add, use fraction manipulatives

(each piece may be labeled with the corresponding unit fraction) to model each fraction and join them to find the sum (e.g., 1/4 + 2/4 = 3/4).

To subtract, use fraction manipulatives (each piece may be labeled with the corresponding unit fraction) to model the first fraction in the expression and remove manipulatives that represent the fraction being subtracted(e.g., 3/4 - 2/4 = 1/4).

Create a pictorial representation of the word problem.

Use context clues to interpret the concepts, symbols, and vocabulary for addition and subtraction.

To add, use a visual representation of a whole divided into equal pieces (each piece may be labeled with the corresponding unit fraction). Shade each unit to represent the fractions in the expression and count the shaded units to find the sum.

To subtract, use a visual representation of the first fraction in the expression. Cross out the piece(s) that represent the fraction being subtracted. Count the remaining piece(s) to find the remainder.

Suggested Instructional Strategies: Teach explicitly how to express a verbal description of a fraction

(“one-fourth” as 1/4). Task Analysis:

o Highlight/circle important words.o Choose the correct operation (+, -, x, ÷).o Compute the answer.o State the answer.

Teach explicitly how to represent the total number of objects in a word problem as an array by creating sets based on the denominator of the

1

Element Cardprovided fraction in a word problem (e.g., 1/2 of the 20 students would be a group of 20 objects shown as two arrays of 10 each.)

Teach explicitly how to use a number line/conversion tables to solve a word problem.

Use *Model/Lead/Test. Give students problems to model such as these: Charlene ate 1/4 of the

sandwich at breakfast and 2/4 of the sandwich at lunch. How much of the sandwich did she eat?

Suggested Supports and Scaffolds: Use arrays to represent the denominator as sets. Number Line Objects to represent arrays and perform operation Rectangular blocks engraved with dots (can be used to teach students who

have visual impairment) Fraction strips Assistive technology Use adapted text for word problems

2

Element Card

FLS: MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

MAFS.5.NF.2.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Access Point NarrativeMAFS.5.NF.2.AP.3a Divide unit fractions by whole numbers and whole numbers by

unit fractions using visual fraction models.MAFS.5.NF.2.AP.7a Divide unit fractions by whole numbers and whole numbers by

unit fractions using visual fraction models.Essential Understandings:

Concrete Understandings Representation MAFS.5.NF.2.AP.3a To show whole numbers divided by

unit fractions, use fraction manipulatives to model the wholes. Use a template to guide placement of the unit fractions to illustrate that every whole can be represented in terms of groups of unit fractions. (e.g., 3 ÷ 1/2 is 3 wholes divided into 6 groups of 1/2).

Understand the following concepts and vocabulary: fraction, whole number, divide, ÷.

Use visual representations to model whole numbers and groups of unit fractions.

Count the number of groups to determine the quotient.

1

Element CardConcrete Understandings Representation


MAFS.5.NF.2.AP.7a To show whole numbers divided by unit fractions, use fraction manipulatives to model the wholes. Use a template to guide placement of the unit fractions to illustrate that every whole can be represented in terms of groups of unit fractions (e.g., 3 ÷ 1/2 is 3 wholes divided into 6 groups of 1/2).


Use visual representations to model whole numbers and groups of unit fractions.


Suggested Instructional Strategies: Task Analysis:

o Place fraction bars labeled with the same unit fraction on top of a whole fraction bar(s) until it is completely covered (e.g., for the expression 2 divided by 1/4, put four 1/4 fraction bars on top of each of the whole fraction bars).

o Move each unit fraction bar off of the whole fraction bar(s) one at a time to form separate groups (use a template for the separate groups, if necessary).

o Count how many groups of that unit fraction were in the dividend (e.g., there were eight groups of 1/4 in 2 wholes.)*Repeat task analysis with circular fraction pieces.

Use food that is easy to divide into equal pieces to divide whole numbers by unit fractions (e.g., cut 3 cookies into halves, pass out the halves to different students until there are no halves left, then count how many groups of 1/2 were made from 3 whole cookies. 6 people got 1/2 of a cookie, so 3 divided by 1/2 is equal to 6.)

2

Element Card

Suggested Supports and Scaffolds: Templates Number Lines SMART Board Technology Graph paper Food that is easy to divide into equal pieces (apples, cupcakes, cookies,

etc.) Fraction bars Assistive technology

3

Element Card

FLS: MAFS.5.NF.2.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

MAFS.5.NF.2.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Access Point NarrativeMAFS.5.NF.2.AP.4a Multiply a fraction by a whole or mixed number using visual

fraction models.MAFS.5.NF.2.AP.6a Multiply a fraction by a whole or mixed number using visual

fraction models.


Place fraction manipulatives in groups as indicated by the whole number in a given multiplication expression (e.g., 2 x 1/3 = 2 groups of 1/3 or 3 x 1/4 = 3 groups of 1/4).

Use repeated addition/skip counting to find the product (e.g., 1/3 + 1/3 = 2/3 or 1/4 + 1/4 + 1/4 = 3/4).

Use a visual representation of a whole divided into equal pieces (each piece may be labeled with the corresponding unit fraction). Shade the number of groups of the fraction (e.g., 3 groups of 1/5) as indicated by the whole number.

Use repeated addition/skip counting to find the product(e.g., 1/5 + 1/5 + 1/5 = 3/5).

Understand the following vocabulary: numerator, denominator.

Suggested Instructional Strategies: *Model/Lead/Test

1

Element Card

ModelSteps/Materials Teacher Says/Does Student


Teacher:Fraction Bars

“I can use fraction bars to multiply a fraction by a whole number.”

Make an array by placing fraction bars in rows as indicated by the whole number in a given multiplication expression (e.g. 2 x 1/3 = 2 rows of 1/3, so lay down a fraction bar labeled 1/3 and say, “This is one group of 1/3,” and then lay down another fraction bar labeled 1/3 directly underneath it and say, “This is another group of 1/3”. Then say, “We have two groups of 1/3.”)

Student watches.


Use counting or repeated addition to find the product of the multiplication expression. (e.g., For counting, point to each fraction bar one at a time and say, “one third, two thirds. So, 2 x 1/3 is two thirds.”) For repeated addition, point to each fraction bar one at a time and say, “One third plus one third is equal to two thirds. So, 2 x 1/3 is two thirds.”)

Student watches.


2

Element CardSteps/Materials Teacher Says/Does Student


Teacher and Student:Fraction Bars

“We can use fraction bars to multiply a fraction by a whole number.”Demonstrate making an array by placing fraction bars in rows as indicated by the whole number in a given multiplication expression (e.g. 2 x 1/3 = 2 rows of 1/3, so lay down a fraction bar labeled 1/3 and say, “This is one group of 1/3,” and then lay down another fraction bar labeled 1/3 directly underneath it and say, “This is another group of 1/3”. Then say, “We have two groups of 1/3.”)

Student lays down fraction bars to show the same multiplication array modeled by the teacher. Student points to/counts each group of the fraction.

“Good job modeling the multiplication expression and counting each group.”

Demonstrate using counting or repeated addition to find the product of the multiplication expression. (e.g., For counting, point to each fraction bar one at a time and say, “one third, two thirds. So, 2 x 1/3 is two thirds.”) For repeated addition, point to each fraction bar one at a time and say, “One third plus one third is equal to two thirds. So, 2 x 1/3 is two thirds.”)

Student uses counting or repeated addition to find the product of the multiplication expression. Say/select the correct product.

“Good job using counting/repeated addition to find the product.”

Lead

3

Element Card

TestSteps/Materials Teacher Says/Does Student Response Teacher

FeedbackStudent:Fraction Bars

“Use fraction bars to multiply a fraction by a whole number.”“Lay your fraction bars on the array (template)”

Student lays down fraction bars to show the multiplication expression requested by teacher. Student points to/counts each group of the fraction.

“Good job modeling the multiplication expression and counting each group.”



“Count or use repeated addition to find the product.”

Student uses counting or repeated addition to find the product of the multiplication expression. Say/select the correct product.

“Good job using counting/repeated addition to find the product.”



Repeat the *Model/Lead/Test with fractions that are not unit fractions. (e.g., for 2 x 2/5, lay two 1/5 fraction bars side by side to show one group of 2/5, and then lay two 1/5 fraction bars side by side directly beneath the other 2 fraction bars to show another group of 2/5, then use counting or repeated addition to find the product.)

Pizza Fractions: cut pizza circles the same size then cut them into a variety of labeled unit fractions and use them to multiply a fraction by a whole number by making groups of the fraction and then using counting or repeated addition to find the product. (e.g., for 3 x 1/4, put three groups of 1/4 onto a circle the size of the original circle, and then count 1/4, 2/4, 3/4 or add 1/4 + 1/4 + 1/4 to get 3/4.)

To multiply a fraction by a mixed number (keep in mind that before moving on to this next step, students must first master multiplying a fraction by a fraction, which has not been covered in any prior Access Points):

4

Element Cardo Use a template and fraction bars or circular fraction pieces to convert

the mixed number to a fraction greater than one (e.g., 1-1/8 is 8/8 + 1/8, which is 9/8.)

Image link Use graph paper and colored pencils/stickers to multiply a fraction by a

fraction using an array.

Image link

Suggested Supports and Scaffolds: Circular fraction pieces (including wholes) Fraction bars Templates Graph paper Assistive technology iPad applications

5

http://aescubs5thgrade.weebly.com/multiplying-fractions.html

http://www.education.com/slideshow/introduction-improper-fractions/

Element Card

FLS: MAFS.5.NF.2.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other

factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product

greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Access Point NarrativeMAFS.5.NF.2.AP.5a Determine whether the product will increase or decrease based on

the multiple using visual fraction models.Essential Understandings:

Concrete Understandings Representation Use fraction manipulatives and begin with single

groups of a number (e.g., 1 × 5, 1 × 6, 1 × 7) to show the product will remain the same.

Use fraction manipulatives to model groups of numbers greater than 1 (e.g., 2 × 5, 3 × 6, 4 × 7) to show the product will increase.

Use fraction manipulatives to model groups of a numbers less than 1 (e.g., 1/2 × 6, 1/2 × 4) to show the product will decrease.

Recognize when a number is multiplied by a number less than one (e.g., 1/2, 3/4, 5/6, 0) the product will decrease.

Recognize when a number is multiplied by a number greater than one, the product will increase.

Understand the following vocabulary: product, increase, decrease, and fraction.

Suggested Instructional Strategies: Explicitly teach that a multiplicand multiplied by a whole number multiplier

increases the product and a fraction/decimal multiplier decreases the product; demonstrate a strategy for self-checking the answer.

Task Analysis example:o State the problem using a whole number multiplier.o Predict if the product will increase or decrease.o Show me one set of (X) chips. Count the chips. How many?o Now show me two sets of (X) chips. Count the chips. How many?o State the total number of chips.o Student states if the product is greater or less than the multiplicand.

Task Analysis example:o State the problem using a fraction multiplier.o Predict if the product will increase or decrease.o Provide a set of total number of chips to be divided by a fraction.o Model the number of created sets.o Student states if the product is greater or less than the multiplicand.

Use counting strategies. Use number patterns (i.e., skip counting). Modeling problem solving with supports. Show multiplication as repeated addition (write 3 x 3 as 3 + 3 + 3).

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Suggested Supports and Scaffolds: Counters (chips) Picture and objects Number Line Fraction strips and tables Decimal tables Multiplication table or calculator to self-check answers Graphic organizers (rows and columns)

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FLS: MAFS.5.MD.1.1 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Access Point NarrativeMAFS.5.MD.1.AP.1a Convert standard measurements of time to solve real-world

problems.


Use tools to demonstrate knowledge of how many seconds are in a minute; minutes are in an hour; hours are in a day.

Use tools to demonstrate knowledge of how many days are in a week; weeks in a month; months in a year.

Use tools to locate specific intervals of time (i.e., one week from this date).

Use daily schedule as a reference when solving problems involving intervals of time (e.g., It is 8:00 AM. Activity is at 10:00 AM. How many hours until activity? If you know there are 60 minutes in an hour, how many minutes until activity?)

Use a calendar as a reference when solving problems involving intervals of time (e.g., It is August 31. How many days until October 1?)

Understand the vocabulary for: seconds, minutes, hours, days, weeks, months, years, calendar, AM, and PM.

Understand the number(s) on the left represents the hour and numbers on the right represent minutes for digital clock time.

Demonstrate the progression of a calendar (i.e., days in a week, months in a year).

Demonstrate that as units of measurement get larger

(i.e., minutes hours), the number gets smaller(i.e., 60 minutes 1 hour).

Suggested Instructional Strategies: Teach explicitly by modeling how to use a calendar, with students following

along with individual calendars, noting that:o There are 7 days in a weeko Varied number of weeks in a montho There are 12 months in a year

Teach explicitly by modeling the motion and progression of the clock, with students following along with individual manipulative clocks, noting that:

o There are 60 seconds in a minuteo There are 60 minutes in an houro There are 24 hours in a day

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Element Card Forward chaining:

o Use manipulative clocks to demonstrate the knowledge of intervals of time. For example:

It is 8:00 AM. Make your clock show 8:00. Activity is at 10:00 AM. Count the number of hours between 8

and 10. How many hours until activity? If you know there are 60 minutes in an hour, how many

minutes until activity?o Use calendars to demonstrate the knowledge of intervals of time. For

example: It is August 31. How many days until October 1? How many

weeks until October 1? What is three weeks from April 4? How many days would that

be? The month is June. How many months until it is September? How

many weeks would that be? Provide a calendar. The teacher says there are seven days in one week and

counts out each day (1-7) and points to the calendar. Say, “Show me one week.” Say, “There are seven days in one week for a ratio of 7:1 (days: week). So, how many days are in three weeks?” “If you have to write two book reports per week, how many book reports will you write in four weeks?”

Use plastic fraction bars to make equivalent measurements. For example, shade a picture a ruler into twelve portions and use the fraction bars to visually illustrate the equivalent of 6 inches (6/12) and one foot (12/12).

Students can solve a one-step problem by using manipulatives and/or incorporating symbolic numeral cards to correspond to a concrete model. For example, the teacher can give a problem such as “The bookshelf is 2 feet long. There are 12 inches in one foot. How many inches is the bookshelf altogether?” Then have students solve this problem by using objects. The students count out 24 objects.

Supports and Scaffolds: Manipulative clocks Stopwatch/timer Calendar where days/months can be manipulated Daily schedule with digital or analog times: Click here Schedule activities to be held throughout a month: Click here

2

http://www.abcya.com/calendar_word_problems.htm

http://www.abcya.com/months_of_the_year.htm

Element Card Calculator Counters and graphic representation of ratios and fractions Worksheet with partially completed formula Interactive Whiteboard or PowerPoint Balance or scale Clock Counting tiles Cups and buckets to measure volume

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FLS: MAFS.5.MD.1.1 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Access Point NarrativeMAFS.5.MD.1.AP.1b Convert standard measurements of length to solve real-world problems.


Use tools to demonstrate knowledge of how many inches are in a foot; feet are in a yard.

Use tools to demonstrate knowledge of how many centimeters are in a meter.

Use tools (i.e., yardstick, ruler) as a reference when solving problems involving length (e.g., Your desk is 2 feet wide. There are 12 inches in 1 foot. How many inches wide is your desk?).

Understand standard units and abbreviations (e.g., feet = ft).

Understand concepts and vocabulary: conversion, inch, foot, yard, centimeter, and meter.

Demonstrate that as units of measurement get larger (i.e., inches feet), the number gets smaller (i.e., 12 inches 1 foot)

Suggested Instructional Strategies: *Multiple Exemplar Training (e.g., “This is an inch, this is an inch…this is not an

inch, show me an inch.”) Task Analysis steps to convert from inches to feet using a table Teach student to use proportions (e.g., 12:1, 12 inches = 1 foot) to convert the

same measurement from one unit to another. Measure length using one inch increments (how many?) and one foot increments

(how many?) Have students place the U.S. unit cards/representations in order from smallest to

largest.

Suggested Supports and Scaffolds: Conversion table, adapted or unadapted measuring tools Calculator Counting blocks or manipulatives Counting mechanism (e.g., number line) Match measuring tool to unit (e.g., “Identify the tool to measure inches.”) Software Rulers with limited measurement (e.g., only 1 inch and 1/2 inch tabs)

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FLS: FLS: MAFS.5.MD.1.1 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Access Point NarrativeMAFS.5.MD.1.AP.1b Convert standard measurements of length to solve real-

world problems.


Use tools to demonstrate knowledge of how many inches are in a foot; feet are in a yard.

Use tools to demonstrate knowledge of how many centimeters are in a meter.

Use tools (i.e., yardstick, ruler) as a reference when solving problems involving length (e.g., Your desk is 2 feet wide. There are 12 inches in 1 foot. How many inches wide is your desk?).

Understand standard units and abbreviations (e.g., feet = ft).

Understand concepts and vocabulary: conversion, inch, foot, yard, centimeter, and meter.

Demonstrate that as units of measurement get larger (i.e., inches feet), the number gets smaller (i.e., 12 inches 1 foot)

Suggested Instructional Strategies: Teach explicitly how to use a ruler to measure objects

o Present an objecto Present measurement toolso Demonstrate that the choice of measurement tool is based on the size

of the objecto Demonstrate how to line up object to be measured at the beginning of

the ruler/measuring stick, or “0”o Demonstrate how to track from left to right until reaching the end of

the objecto Explain that the number that the object stops on is the total length of

the object Provide students with a task analysis of the process

Step # Action1 Select a measuring tool based on the size of the object to be measured.2 Line the object to be measured at the beginning of the tool, or “0”3 Using your pointer finger, track on the measurement tool from the “0”

or start of the object, to the point on the tool where the object being measured ends.

4 Record the length of the object.

Show multiple objects and have students determine appropriate tool to measure length in inches or feet.

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Element CardObject Tool

banana ruler yardstick

desk ruler yardstick

foot ruler yardstick Use a yardstick to determine lengths in inches or lengths in feet. For

example:o Your desk is 2 feet wide. There are 12 inches in 1 foot. How many

inches wide is your desk?o Measure your foot in centimeters. How long is your foot in

centimeters? How long is your foot in millimeters?

Supports and Scaffolds: Ruler with inches marked Ruler with centimeters marker Yardstick Meter stick Tape measure Conversion table

Inches Feet12 inches 1 foot24 inches 2 feet36 inches 3 feet48 inches 4 fee

t Measuring is an activity for children to practice finding lengths. This

educational activity includes both metric and imperial units. Children can decide between a metric ruler and an imperial ruler and also choose a level of difficulty. Click for link

Measure/estimate lengths using an inch ruler: Click here Formative assessment task and rubric: Converting measurement: Click here

2

http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/65698

https://www.ixl.com/math/grade-4/measure-using-an-inch-ruler

http://www.abcya.com/measuring.htm

Element Card

FLS: FLS: MAFS.5.MD.1.1 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Access Point NarrativeMAFS.5.MD.1.AP.1c Convert standard measurements of mass to solve real-world

problems.


Use tools to demonstrate knowledge of how many grams are in a kilogram.

Use tools (i.e., balance) as a reference when solving problems involving mass (e.g., A paperclip has a mass of one gram. There are 1,000 grams in 1 kilogram. How many paperclips will it take to make a kilogram?)

Understand the following concepts and vocabulary: conversion, kilograms, and grams.

Understand standard units and abbreviations (e.g., grams = g).

Demonstrate that as units of measurement get larger (i.e., grams -> kilograms), the number gets smaller (i.e., 1000 grams 1 kilogram).

Suggested Instructional Strategies: Show multiple objects and have students determine appropriate tool to

measure mass in grams or kilograms.Object Tool

paperclip grams kilograms

kitten grams kilograms

pencil grams kilograms

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Use a scale to solve problems involving mass. For example:o A paperclip has a mass of one gram. There are 1,000 grams in 1

kilogram. How many paperclips will it take to make a kilogram?o A bag of potatoes weighs 2 kilograms. How many grams does the bag

weigh? Use the conversion to help solve problems. A bag of potatoes weighs 2 kilograms. A serving of French fries is 800 grams.

How many servings of French fries can Megan make out of the bag of potatoes?

Supports and Scaffolds: Scales that show weight in grams and/or kilograms. Conversion table

Grams Kilograms1000 grams 1 kilogram2000 grams 2 kilograms

Formative assessment task and rubric: converting measurement

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FLS: MAFS.5.MD.2.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Access Point NarrativeMAFS.5.MD.2.AP.2a Collect and graph fractional data on a line plot (e.g., length

of each person’s pencil in classroom, hours of exercise each week).


Identify a data set based on a single attribute (e.g., pencils vs. markers).

Identify items for a data set with more than one or less than one (e.g., this bar represents a set with more than one).

Organize the data on the line plots using objects that represent one piece of data (e.g., Use tools to measure the length of students’ hands. Using objects, plot measurement data on a line plot.)

Organize collected data on a line plot (e.g., Use tools to measure the length of students’ hands. Plot measurement data on a line plot.).

Identify data set with some number (e.g., how many students’ hands were 5 1/4 inches long?).

Suggested Instructional Strategies:1. Have students identify a something that can be measured using fractional

data (e.g., hand sizes of students, foot sizes of students, etc.)2. Have students measure and record their hand size.3. Using a large piece of paper (rolled out easel paper, etc.), construct a line

plot without the fractional data increments.4. Construct a table to reflect student name and student hand size.

Student Name

Hand Size

Student 1 5 1/8Student 2 5 1/8Student 3 5 1/4Student 4 5 1/2Student 5 5 1/4

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Element Card5. Have student trace their hand on the line plot that represents their hand size

measurement.6. Have students determine a visual representation to reflect what is being

measured (i.e., an X).7. Given a line plot with fractional increments, have students organize the data

on the line plots.

Supports and Scaffolds: Performance assessment: line plots parts 1 and 2: Click here Practice constructing line plots using whole numbers: Click here Practice constructing and interpreting line plots using fractional numbers:

Click here Create line plots: Click here Interpreting line plots: Click here

2

https://www.ixl.com/math/grade-4/interpret-line-plots

https://www.ixl.com/math/grade-4/create-line-plots

https://www.ixl.com/math/grade-4/create-and-interpret-line-plots-with-fractions

http://www2.learningtoday.com/player/swf/Data_Analysis_LinePlots_L3_V1_T1a.swf


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FLS: MAFS.5.MD.3.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Access Point NarrativeMAFS.5.MD.3.AP.3a Use packing to recognize volume of a solid figure.


Identify a rectangular prism using models.

Identify a unit cube given models. Use unit cubes to pack a rectangular

prism.

Identify a rectangular prism using images.

Understand that packing is filling a rectangular prism (i.e., box) with cubes having no gaps or overlaps.

Understand the vocabulary and concepts of unit cubes, solid figure, rectangular prism, volume.

Suggested Instructional Strategies: Teach explicitly attributes of solid figures, namely, rectangular prisms to be

able to identify rectangular prisms in geometric figures and in real world examples.

*Multiple Exemplar Trainingo An array/row: “This is a rectangular prism. This is a cylinder. This is a

rectangular prism. Show me a rectangular prism.”

*Example/Non-Exampleo Show me an example of a rectangular prism. Show me something that

is NOT a rectangular prism.

Practice:o Practice filling boxes with unit cubes.

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Element Cardo Have students count the number of unit cubes to determine how many

cubes it takes to fill the box.o Explain that the number of cubes that it takes to fill the box is the

volume of the box. o Also explain that there are multiple ways to find the volume of a box.

Supports and Scaffolds: Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit

cubes needed to fill the entire box is known as the volume of the box. Can you determine a rule for finding the volume of a box if you know its width, depth, and height? Click for link to activity

By the end of this tutorial, you will be able to demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume. Click for link to activity

Filling layers of a rectangular prism to find volume. Click for link to activity

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http://www.learner.org/interactives/geometry/area_volume.html

http://www.cpalms.org/Public/PreviewResourceUpload/Preview/119127


http://illuminations.nctm.org/Activity.aspx?id=4095

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FLS: MAFS.5.MD.3.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Access Point NarrativeMAFS.5.MD.3.AP.4a Determine the volume of a rectangular prism built by “unit

cubes.”


Count unit cubes used to pack a rectangular prism to determine volume.

Understand the vocabulary and concepts of unit cubes, solid figure, rectangular prism, volume.

Identify the numeral representing the quantity of cubes inside the rectangular prism.

Suggested Instructional Strategies: Teach explicitly how to fill a rectangular prism by putting unit cubes in the

object without gaps or overlaps. Provide an example and non-example of a rectangular prism filled with unit

cubes without gaps or overlaps and with gaps and overlaps.

Use unit cubes to build three-dimensional models to represent rectangular prisms. (Instructional implications as described on CPALMS)

o Review the concept of the volume of a rectangular prism and finding volume by counting the number of unit cubes it takes to fill the prism.

o Emphasize that the unit of measure of volume is a single cube so that the volume of a 2 x 3 x 5 prism can be described as 30 cubes or 30 cubic units.

o Practice applying the formula by counting out the number of unit cubes for the length, width, and heightV = Length (# of cubes) x Width (# of cubes) x Height (# of cubes)

o Explain that if each cubic unit has edges that measure 1 inch, then each cubic unit contains 1 cubic inch of volume so that the total volume of the prism is 30 cubic inches.

o Then transition the student to using a volume formula, using manipulatives or visual representation as necessary.

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Element Cardo Guide the student to count layers of unit cubes to derive a formula for

the volume of a rectangular prism and to write the formula as either V = l x w x h or V = B x h where B is the area of the base.

Supports and Scaffolds: Formative assessment for interpreting and determining volume. (Use

manipulatives to find the volume.) Click for link Activity: create a cubic meter, or other unit. Click for link Volume calculator Click for link Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit

cubes needed to fill the entire box is known as the volume of the box. Click for link

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http://mathcentral.uregina.ca/volume_calculator

http://www.k-5mathteachingresources.com/support-files/build-a-cubic-meter.pdf


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FLS: MAFS.5.MD.3.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V=l x w x h and V= B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Access Point NarrativeMAFS.5.MD.3.AP.5a Use multiplication to represent each layer of the rectangular

prism.


Use unit cubes to fill a rectangular prism.

Count to determine how many unit cubes are in one row of a layer.

Count to determine how many unit cubes are in one column of a layer.

Use multiplication or repeated addition to determine the total number of unit cubes in one layer (area of the base or B).

Understand the vocabulary and concepts: row, column, layer, unit cubes, solid figure, rectangular prism, and volume.

Use a visual representation to determine how many unit cubes are in one row of a layer.

Use a visual representation to determine how many unit cubes are in one column of a layer.

Use multiplication or repeated addition to determine the total number of unit cubes in one layer (area of the base or B).

Suggested Instructional Strategies: Teach explicitly how to fill a rectangular prism without gaps and overlaps.

o Fill the prism with unit cubeso Count one row of a layer (length)o Count one column of a layer (width)o Use learned strategies (arrays, repeated addition, multiplication) to

determine the total number of unit cubes in one layero Explain that the total number of unit cubes in one layer is the area of

the base of “B”)

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Element CardOne Row One Column Number of Layers

Length = 3 (1 row of 3 cubes) Width = 2 (2 columns) Height = 5 cubes Area = l x w

o Area of one layer = 3 x 2 (multiplication)o Area of one layer = 3 + 3 (repeated addition)o Area of one layer = 6

Number of layers to fill the prism = heighto Number of layers to fill the prism = 5

Volume = length x height (B) x height (h)o Volume = 3 x 2 x 5 (multiplication)

(3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) = 30o Or volume = 6 x 5 (repeated addition)

6 + 6 + 6 + 6 + 6 = 30Use unit cubes to build three-dimensional models to represent rectangular prisms. (Instructional implications as described on CPALMS)

Review the concept of the volume of a rectangular prism and finding volume by counting the number of unit cubes it takes to fill the prism.

Emphasize that the unit of measure of volume is a single cube so that the volume of a 2 x 3 x 5 prism can be described as 30 cubes or 30 cubic units.

Practice applying the formula by counting out the number of unit cubes for the length, width, and height

V = Length (# of cubes) x Width (# of cubes) x Height (# of cubes)

Supports and Scaffolds: Formative assessment for interpreting and determining volume. Click for link Volume calculator Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit


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Access Point NarrativeMAFS.5.MD.3.AP.5b Use addition to determine the length, width, and height.


Identify a composite three-dimensional (3-D) figure (i.e., two or more rectangular prisms put together).

Decompose the composite figure into two separate rectangular prisms.

Pack each rectangular prism with unit cubes.

Find the volume of figure a (e.g., by counting all of the unit cubes); find the volume of figure b; add the two volumes together.

Understand the vocabulary and concepts: volume, composite 3-D figure, decompose, rectangular prism, length, width, height.

Use a visual representation of a composite figure to determine the total volume of figure a and figure b combined.

Suggested Instructional Strategies: Give concrete experiences with composite rectilinear figures.

o Give a student a composite rectangular prism.o Have students break apart (decompose) the composite figure into two

separate figures.o Have the students add the volume from figure 1 to figure 2.o Have students put the two figures back together (compose) to make

the connection that volume is additive.o Have students determine the number of cubes by counting the number

of cubes that make up the composite rectilinear figure Give students opportunities to take figures apart and count the unit cubes:

o as a composite rectilinear figure

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Element Cardo as two separate rectangular prismso record the volume of the composite rectilinear figureo record the volume of the two separate rectangular prismso compare the volume to demonstrate the understanding that the

volume is additive.For example:

Composite Figure

=Rectangular Prism A

+

Rectangular Prism B

Total Volume of Composite

FigureEquals Volume of Figure

A Plus Volume of Figure B

Supports and Scaffolds: Unpacked 5th grade standards pages 50-51. Click for common core link Activity: use unit cubes to create different composite figures with the same

volume. Click for activity link

2

http://www.k-5mathteachingresources.com/support-files/3d-structures.pdf

http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf

Element Card





Access Point NarrativeMAFS.5.MD.3.AP.5c Connect the layers to the dimensions and multiply to find the

volume of the rectangular prism.


Use unit cubes to fill one layer (base) of the rectangular prism.

Use the unit cubes to find the area of the base layer

Determine the number of layers needed to fill the rectangular prism.

Use the area of the base and the number of layers (height) to find the volume of the rectangular prism by multiplying or using repeated addition.

Recognize the formula for finding volume: V= l × w x h

Relate the concrete model to the formula V= B x h; where B = area of the base

Suggested Instructional Strategies: Use unit cubes to build three-dimensional models to represent rectangular

prisms. (Instructional implications as described on CPALMS)o Review the concept of the volume of a rectangular prism and finding

volume by counting the number of unit cubes it takes to fill the prism. o Emphasize that the unit of measure of volume is a single cube so that

the volume of a 2 x 3 x 5 prism can be described as 30 cubes or 30 cubic units.

o Practice applying the formula by counting out the number of unit cubes for the length, width, and height

o V = Length (# of cubes) x Width (# of cubes) x Height (# of cubes)o Explain that if each cubic unit has edges that measure 1 inch, then

each cubic unit contains 1 cubic inch of volume so that the total volume of the prism is 30 cubic inches.

o Then transition the student to using a volume formula, using manipulatives or visual representation as necessary.

1

Element Cardo Guide the student to count layers of unit cubes to derive a formula for

the volume of a rectangular prism and to write the formula as either V = l x w x h or V = B x h where B is the area of the base.

Practice strategies to find the volume:o Application of the formula for volume [Volume = length x height (B) x

height (h)] 3 x 2 x 5 = 30

o Multiplication (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2)+ (3 x 2) = 30

o Repeated addition 6 + 6 + 6 + 6 + 6 = 30

Supports and Scaffolds: Formative assessment for interpreting and determining volume. Click for link Volume Calculator Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit


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Element Card

FLS: MAFS.5.G.1.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).Access Point NarrativeMAFS.5.G.1.AP.1a Locate the x- and y-axis on a coordinate plane.MAFS.5.G.1.AP.1b Locate points on a coordinate plane.MAFS.5.G.1.AP.1c Graph ordered pairs (coordinates).


MAFS.5.G.1.AP.1a Identify the x- and y-axes on a tactile (i.e., raised gridlines) graph.

Identify the origin (i.e., point of intersection of the x- and y-axes) on a tactile graph.

Understand the following concepts and vocabulary: x-axis, y-axis, graph, origin, point of intersection, horizontal, and vertical.

Identify the x- and y-axes on a graph.

MAFS.5.G.1.AP.1b Identify the x- and y-axes. Identify the origin (i.e., point of intersection

of perpendicular lines). Locate a given point on a coordinate plane

(e.g., show me point A). Use tools (e.g., use craft sticks to extend the

point to the axis) to identify an ordered pair as an x-coordinate followed by a y-coordinate.

Understand the following concepts and vocabulary: origin, axis, grid, point, x-axis, y-axis, point of intersection.

Identify an ordered pair as an x-coordinate followed by a y-coordinate.

MAFS.5.G.1.AP.1c Identify the x- and y-axes. Identify the origin (i.e., point of intersection

of perpendicular lines). Identify that an ordered pair:

o The first coordinate is the location on the x-axis

o The second coordinate is the location on the y-axis.

o The coordinates are written in parentheses and separated by a comma (3,2)

Complete concrete graphing of ordered pairs. (e.g., Use a manipulative to move three spaces across the x-axis, then 2 spaces up the grid; mark the point)

Understand the following concepts and vocabulary: coordinates, ordered pair, origin, axis, grid, point, parentheses, and comma.

Graph ordered pairs on a coordinate plane.

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Element Card

Suggested Instructional Strategies: Teach explicitly through a hands-on graphing activity as provided by CPALMS

(Click for link)o Create a giant coordinate grid on the floor in your classroom (his works

very well if you have a tile floor).o Mark the grid with painters tape and use index cards to number the

x-axis and y-axis.o Place dots with student names on the giant coordinate grid.o Call the students by name to prevent a mad rush. Tell them that when

you call their name they are to walk over and stand on their dot.o Ask one student to raise their hand and I walk to the big “0” for the

origin and ask, “What do I need to do to reach Chelsea?” Give students a few minutes to process, then explain “To reach Chelsea, I have to walk 5 units along the x-axis (think of the x as across because the lines cross), and now 3 units up If you look at the y-axis you should be in line with the 3 on the y-axis, (tell them to think y to the sky!”)

o As they are taking their turns keep asking, “Which way do you move first? Which way do you move second? When you move along what axis are you on? When you move up what axis are you in line with?”

Teach explicitly the components, vocabulary associated with, and how to label a coordinate plane including:

o Coordinates – a group of numbers used to indicate the position of a point, line, or plane.

o Ordered pair – a pair of numbers where order is important – (4, 6) ≠ (6, 4) and are used to indicate a point on a graph or map.

o Origin – the point where the x- and y-axis intersect on a coordinate plane.

o Axis – a fixed reference line for the measurement of coordinates.o Grid – an object (paper, geoboard) marked with regular lines

(horizontal and vertical) used for graphing.

Supports and Scaffolds: Locating points on a coordinate plane: Click here Locate the “aliens” on a coordinate plane: Click here Graph points on a coordinate plane: Click here You Sank my Battleship! Online tutorial for understanding coordinates: Click

here

2



https://www.ixl.com/math/grade-5/graph-points-on-a-coordinate-plane

http://www.mathplayground.com/locate_aliens.html

https://www.ixl.com/math/grade-5/coordinate-graphs-review-whole-numbers-only

http://www.cpalms.org/Public/PreviewResource/Preview/49870

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FLS: MAFS.5.G.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Access Point NarrativeMAFS.5.G.1.AP.2a Find a location on a map using given coordinates.


Identify the x- and y-axes on a map. Identify the origin (i.e., point of

intersection of perpendicular lines) on a map.

Locate a given point on a map (e.g., show me point A on the map).

Use tools (e.g., use craft sticks to extend the point to the axis) to identify an ordered pair as an x-coordinate followed by a y-coordinate.

Understand the following concepts and vocabulary: coordinates, ordered pair, origin, axis, grid, point, up, down, over

Given a visual diagram, locate the coordinate values of an item.

Use a map to find a given location.

Suggested Instructional Strategies: Practice finding locations on math and applying coordinate-plane knowledge

to real-world problems. For example:o Using the coordinate grid, which ordered pair, represents the location

of the school?o Using the coordinate grid, which ordered pair, represents the location

of the park?o Explain a possible path from the park to the library.

Supports and Scaffolds: Coordinate graphs as maps. Click for link

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https://www.ixl.com/math/grade-4/coordinate-graphs-as-maps

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FLS: MAFS.5.G.2.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

MAFS.5.G.2.4 Classify two-dimensional figures in a hierarchy based on properties.

Access Point NarrativeMAFS.5.G.2.AP.3a Recognize properties of simple plane figures using polygon-

shaped manipulatives.MAFS.5.G.2.AP.4a Use polygon-shaped manipulatives to classify and organize two-

dimensional figures into Venn diagrams based on the attributes of the figures.


MAFS.5.G.2.AP.3a Use models and manipulatives to show properties of plane figures (i.e., two-dimensional figures).

Sort shapes by a single attribute (e.g., shapes that have 3 sides vs. shapes that have 4 sides; shapes that have straight edges vs. shapes that have curved edges).

Understand the vocabulary and concepts of plane figure properties: simple plane figure (i.e., rectangle, square, trapezoid, triangle, rhombus, octagon, pentagon, hexagon) angles, sides, lines, vertices, edges, curve, and straight.

Use two-dimensional shapes to point out properties of plane figures (find a right angle in this figure).

MAFS.5.G.2.AP.4a Use models and manipulatives to show properties of plane figures.

Sort two-dimensional figures based upon their properties.

Place sorted two-dimensional figures onto Venn diagram template (e.g., create a Venn diagram from hula hoops).

Understand the vocabulary and concepts of plane figure properties: simple plane figure (i.e., rectangle, square, trapezoid, triangle, rhombus, octagon, pentagon, hexagon) angles, sides, lines, vertices, edges, curve, straight, and Venn diagram.

Match plane figures to figures with like properties and add matched figures to the Venn diagram.

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Suggested Instructional Strategies: Sort polygons based on specified attributes (e.g., place polygons specified

number of sides here, place polygons with specified number of angles here) Identify polygons in the environment. Use Example/Non-example of shapes that are/are not polygons. Match the same to classify shape (e.g. polygons by the number of sides) Use a Geoboard or objects (toothpicks) to make polygons. Have students

identify different attributes (angle, sides) Use a Venn diagram to classify and organize two-dimensional figures based

on attributes.

Link to image

Suggested Supports and Scaffolds: Tangram Sets Shape Blocks Assistive technology Interactive Whiteboard Real world application Objects for creating shapes (e.g., popsicle sticks, pipe cleaners) Computer software Geoboard Graphic organizer for classification

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http://www.math.com/school/subject3/lessons/S3U2L3DP.html

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